# Problems on Ages Quiz Set 003

### Question 1

The ratio of present ages of two monuments A and B is \$4{1/2}\$. After 7 years later the age of A will be 88 years. What is the present age of B?

A

18 years.

B

16 years.

C

14 years.

D

20 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${9/2}\$, which is same as: \$4{1/2}\$. So we can write the present ages of A and B, respectively, as 9r and 2r years. 7 years later the age of A is \$9r + 7 = 88\$ which gives r = 9. The age of B, therefore, is 2r = 2 × 9 = 18 years.

### Question 2

Each year the ages of three friends are in an AP(arithmetic progression). The age of middle friend today is 27 years. What would be the sum of their ages 10 years from now?

A

111 years.

B

112 years.

C

110 years.

D

113 years.

Soln.
Ans: a

Let the present ages of the three friends be a - d, a and a + d. As of today a = 27. Ten years later their ages would be a + 10 - d, a + 10, a + 10 + d. Adding these we get 3a + 30 which equals 3 × 27 + 30 = 111 years.

### Question 3

My father was 32 years old when I was born. My mother's age was 32 when my sister, who is 6 years younger to me, was born. What is the difference between the ages of my parents?

A

6 years.

B

7 years.

C

5 years.

D

8 years.

Soln.
Ans: a

If the age of my father is F, then my age is F - 32, so my younger sister's age is (F - 32) - 6, which is = F - 38. If my mother's age is M, then M = (my sister's age) + 32, i.e., M = (F - 38) + 32. We get F - M = 6 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 32 + 6 = 38. At the time my mother was 32 years. So the difference between their ages = 38 - 32 = 6 years.

### Question 4

The sum of ages of two friends is 13, whereas the product of their ages is 42. What is the sum of squares of their ages?

A

85 years.

B

86 years.

C

84 years.

D

87 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 13, and xy = 42. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 13^2 - 2 × 42\$ = 85.

### Question 5

The ratio of present ages of two monuments A and B is \$2{1/4}\$. After 3 years later the age of A will be 102 years. What is the present age of B?

A

44 years.

B

40 years.

C

36 years.

D

48 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${9/4}\$, which is same as: \$2{1/4}\$. So we can write the present ages of A and B, respectively, as 9r and 4r years. 3 years later the age of A is \$9r + 3 = 102\$ which gives r = 11. The age of B, therefore, is 4r = 4 × 11 = 44 years.